Preheat oven to 350 degrees.
Chop melon into small cubes and cut cherry tomatoes into quarters. Finely dice the onion.
Combine melon, cherry tomatoes and onion in a small bowl. Toss with olive, lemon juice and basil. Season with salt and pepper, to taste. Set aside to let flavors meld.
Heat oil in a large ovenproof skillet over medium-high heat. Season salmon pieces with salt and pepper. Place them in skillet, skin side down. Cook without moving, pressing gently on fillets with a spatula to ensure skin is in full contact with pan, until skin is golden and crisp, about 5 minutes. Transfer skillet to oven (do not turn fish over) and roast until salmon is just opaque in center, 3-4 minutes for medium-rare (time will depend on thickness of fish and desired doneness). Remove salmon from oven and break into smaller pieces. Divide between two plates and top with tomato melon salad.